You are given: (i) The number of claims follows a binomial distribution with parameters m and q. (ii) Claim sizes follow a lognormal distribution with parameters: = 1, and . (iii) The number of claims and claim sizes are mutually independent. (iv) The full credibility standard is such that the observed total amount of claims is to be within 5% of the expected total amount of claims with a probability of 95%. (v) The expected number of claims required for full credibility is 3800. Determine the value of q.